2 Answers
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No, περἰ does not normally have the meaning as an offering for. Purely on the basis of the Greek present, it is hard to translate περἰ in that way.

The standard translations of περἰ + genitive are as follows:

around, about, or near a place

about, concerning

about, on account of

for (as in, to fight for one's life)

of motive (as in, for the sake of victory)

You could make this verse fit any of the last four meanings. (My source for these definitions is Liddell and Scott's Greek-English Lexicon Abridged Edition, which is admittedly more a resource for classical Greek than biblical, but which is probably apt in any case.)

With that said, however, some scholars have made the argument that περἰ ἁμαρτἰας as a phrase has a set meaning. In, for instance, the LXX of Leviticus 5.9, we come across the following bit of Greek:

Here, περὶ τῆς ἁμαρτίας means precisely sin-offering. The phrase is a set phrase that appears in other places in the Septuagint, as a translation for the Hebrew lechatta'th (sin-offering). It seems quite likely that Paul intended this allusion when he wrote Romans 8.3. I'm not sure that it's strong enough to be the principal translation, but there's a very strong case for including it as a footnote.

Now where remission of these [is, there is] no more offering for sin (περὶ ἁμαρτίας).

Essentially, περἰ ἁμαρτἰας is functioning as a substantive prepositional phrase, thus "that which is for sin," i.e. a sin offering. It's likely that Koine Greek simply didn't have an equivalent word for the Hebrew word חטאת; therefore, the Jewish authors had to employ the prepositional phrase περἰ ἁμαρτἰας as a substantive.